A crucial issue in the theory of science education at present is the problem of how much it is possible to generalize about steps in understanding achieved by different pupils in a given topic. Many Piagetians believe that there are qualitatively different steps followed in the same succession by all pupils: some Ausubelians believe that there is no such order, and that for each pupil the best criterion for the teacher is the pupil's present knowledge. One purpose of this study is to shed light on this issue. The study to be described made use of three inputs. The development of a technique of ‘psychometrising Piaget’ by an English team based at London University provided a way of extending a study by Erickson (1977) of personal conceptual inventories to testing a sample of 200 children by a 68 item demonstrated group-test. In addition a team of curriculum developers had provided a tentative list of objectives for the teaching of Heat to Middle School students. The schools in which the study was carried out wished to know which of the objectives were more suitable for 9 or for 12 year-olds. The group-test utilized descriptors both from the Erickson study and from the list of curriculum objectives. In addition to the Heat test a Piagetian group-test (NFER, 1979) in the area of Volume and Heaviness was administered to see whether the development of concepts of Heat could be mapped onto Piagetian stages of development. Test-items in nine aspects of heat were written, with some of the experiments to be demonstrated to the class. These aspects included Conduction, Expansion, Composition of Heat, Temperature Scales, Changes of State, etc. Factor analysis of the data showed that one factor was sufficient to explain the common-factor variance of the heat scales, and that the Heat test was also unifactor with the Piagetian test. It was possible to describe Early Concrete, Late Concrete and Early Formal levels of understanding in the area of Heat and Temperature. In this particular case it appears that the hypothesis of a number of different developmental paths, dependent on previous experience, cannot be sustained. It is not claimed that this would be true of all cognitive development, particularly where culture-specific myths may be involved.